There are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?

Option
1) 3200
2) 3600
3) 2400
4) None of these

• 5 subjects can be arranged in 6 periods in 6P5 ways.
  Remaining 1 period can be arranged in 5P1 ways.
  Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
  Total number of arrangements = (6P5 x 5P1)/2! = 1800
  
  Alternatively this can be derived using the following approach.
  5 subjects can be selected in 5C5 ways.
  Remaining 1 subject can be selected in 5C1 ways.
  These 6 subjects can be arranged themselves in 6! ways.
  Since two subjects are same, we need to divide by 2!
  Total number of arrangements = (5C5 × 5C1 × 6!)/2! = 1800
• 8 years agoHelpfull: Yes(25) No(2)
• ans: 3600
  we have to arrange 5 subjects in 6 periods so 6P5=720
  And we have one more period to assign the class. That means we have 5 possibilities to arrange the remaining period so total possibilities are
  6P5 * 5=720*5=3600
• 8 years agoHelpfull: Yes(18) No(13)
• 5 subjects can be arranged in 6 periods in 6P5 ways.
  Remaining 1 period can be arranged in 5P1 ways.
  Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
  Total number of arrangements = (6P5 x 5P1)/2! = 1800
  
  Alternatively this can be derived using the following approach.
  5 subjects can be selected in 5C5 ways.
  Remaining 1 subject can be selected in 5C1 ways.
  These 6 subjects can be arranged themselves in 6! ways.
  Since two subjects are same, we need to divide by 2!
  Total number of arrangements = (5C5 × 5C1 × 6!)/2! = 1800
• 8 years agoHelpfull: Yes(3) No(1)
• here 6 period and 5 subjects present so
  5 period 5 sub we assign as 5| and 6th period in 5 different ways so
  5*(5!)=600
• 9 years agoHelpfull: Yes(2) No(15)
• http://www.careerbless.com/aptitude/qa/discuss/permutations_combinations/discussion00000024322.php
  
  correct ans 1800
• 7 years agoHelpfull: Yes(1) No(0)
• 5 subjects can be arranged in 6 periods in 6P5 ways.
  Remaining 1 period can be arranged in 5P1 ways.
  Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid double count.
  Total number of arrangements = (6P5 x 5P1)/2! = 1800
• 7 years agoHelpfull: Yes(1) No(1)
• there are total 5 places and in each place we can arrange in 6! ways
• 8 years agoHelpfull: Yes(0) No(4)